1) During the SSLG election, a ballot box contains 30 valid ballots for the position of Grade 10 Representative. Out of these ballots, 12 are votes for Candidate A, 10 are votes for Candidate B, and the rest are votes for Candidate C. If one ballot is randomly selected from the box for verification, what is the probability that the ballot selected is a vote for Candidate A or Candidate B? a) 22/30 b) 11/15 2) What is the probability of an impossible event? a) 0 b) greater than 1 3) During the Regional Association Athletics Meet held in Batangas City, the organizing committee prepared 40 medals for a particular event. Out of these medals, 18 are gold, 12 are silver, and 10 are bronze. If one medal is randomly selected from the medal table for inspection, what is the probability that the medal selected is either gold or bronze? a) 7/10 b) 7/20 4) A player draws one card from a standard deck of 52 cards. Event A is drawing an ace, and event B is drawing a red card. Are these two events mutually exclusive? Why? a) Yes b) No 5) Which pair of events is mutually exclusive? a) Drawing a red card and a heart b) Drawing a king and drawing an ace 6) Which of the following correctly describes mutually exclusive events? a) They have equal probabilities b) They cannot occur at the same time 7) Which statement about P(A ∪ B) is always true? a) It includes outcomes from both events b) It equals 1 for all events 8) Which formula gives the probability of A or B happening if there is no intersection between events A and B? a) P(A ∪ B) = P(A) + P(B) − P(A ∩ B) b) P(A ∪ B) = P(A) + P(B) 9) If P(A) = 0.72, P(B) = 0.65, and P(A ∩ B) = 0.48, what is P(A ∪ B)? a) 0.79 b) 0.89 10) Event A is the probability that a student passes English, and event B is the probability that the student passes Mathematics. Which situation is represented by P(A ∪ B)? a) Passing both English and Math b) Passing English or Math 11) Why must P(A ∩ B) be subtracted when computing P(A ∪ B)? a) To reduce the sample space b) To avoid double counting shared outcomes 12) Which formula correctly represents the probability of the union of two events A and B if A and B are events in the sample space? a) P(A ∪ B) = P(A) + P(B) b) P(A ∪ B) = P(A) × P(B) 13) Why is it important to clearly identify the intersection when illustrating sets using a Venn diagram? a) To know the total number of students b) To avoid counting students more than once 14) In a school program, 3 students are chosen to hold different flags on stage. How many different ways can the 3 students stand in a line?many different ways can the 3 students stand in a line? a) 3 b) 6 15) Which of the following represents the number of permutations of n distinct objects taken r at a time?taken r at a time? a) 𝑛!/r! b) nPr= n!/(n-r)! 16) A student leader needs 2 officers to arrange the booth design for the Batangas City Division Festival of Talents. If there are 5 qualified students and the order of choosing matters, which expression correctly represents the number of possible pairs? a) 5P2 b) 5C2 17) The Math Club will assign 3 students to lead tasks: Registration, Sound System, and Clean-up. There are 4 volunteers, Anna, Ben, Carlo, and Dana. Which statement best explains how to find the number of possible assignments? a) Use 4C3 because only 3 students are needed. b) Use 4P3 because the roles are distinct and order matters. 18) During a school event, a student committee needs to arrange 4 different band performers in a specific order for the program. If only 3 performers will be chosen for the lineup, how many different possible lineups are there? a) 4 b) 24 19) How many permutations can be formed from 4 different cultural dance props used by Batangas City High School for the Arts in their presentation? a) 12 b) 24 20) A librarian is arranging 3 different research folders on a shelf. Which of the following correctly represents the number of ways the folders can be arranged? a) 3P3 b) 3C1 21) The SSLG Officers need to assign 3 different roles, usher, program assistant, and timekeeper, to 5 volunteers. Which reasoning correctly identifies the method to compute the number of arrangements? a) Use 5P3 because the roles are distinct and order matters. b) Use 5C3 because only 3 students are chosen. 22) A local art contest in Batangas City requires the judges to select and rank the top 3 artworks from 7 finalists. How many different rankings are possible? a) 210 b) 504 23) A school choir wants to choose 4 performers to sing in a specific order during a city celebration. If there are 6 talented singers to choose from, how many ordered groups of 4 can be formed? a) 360 b) 3600 24) During break time, a student went to the school canteen to buy merienda. There are 3 snack options available: siomai, pansit, and turon. If the student wants to choose 2 snacks, how many different combinations of snacks can be chosen? a) 2 b) 3 25) A group of Grade 10 students plans to form a committee of 4 from 7 volunteers for a community clean-up drive. How many different committees can be formed? a) 35 b) 840
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